Average Error: 0.2 → 0.2
Time: 2.6s
Precision: 64
\[\left(3 \cdot \left(2 - x \cdot 3\right)\right) \cdot x\]
↓
\[x \cdot \left(6 - 9 \cdot x\right)\]
\left(3 \cdot \left(2 - x \cdot 3\right)\right) \cdot x
↓
x \cdot \left(6 - 9 \cdot x\right)
double f(double x) {
        double r910718 = 3.0;
        double r910719 = 2.0;
        double r910720 = x;
        double r910721 = r910720 * r910718;
        double r910722 = r910719 - r910721;
        double r910723 = r910718 * r910722;
        double r910724 = r910723 * r910720;
        return r910724;
}
↓
double f(double x) {
        double r910725 = x;
        double r910726 = 6.0;
        double r910727 = 9.0;
        double r910728 = r910727 * r910725;
        double r910729 = r910726 - r910728;
        double r910730 = r910725 * r910729;
        return r910730;
}

Error

Bits error versus x

Try it out

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Results

Enter valid numbers for all inputs

Target

Original0.2
Target0.2
Herbie0.2
\[6 \cdot x - 9 \cdot \left(x \cdot x\right)\]

Derivation

  1. Initial program 0.2

    \[\left(3 \cdot \left(2 - x \cdot 3\right)\right) \cdot x\]

  2. Taylor expanded around 0 0.2

    \[\leadsto \color{blue}{6 \cdot x - 9 \cdot {x}^{2}}\]

  3. Simplified0.2

    \[\leadsto \color{blue}{x \cdot \left(6 - 9 \cdot x\right)}\]

  4. Final simplification0.2

    \[\leadsto x \cdot \left(6 - 9 \cdot x\right)\]

Reproduce

herbie shell --seed 2019353 
(FPCore (x)
  :name "Diagrams.Tangent:$catParam from diagrams-lib-1.3.0.3, E"
  :precision binary64

  :herbie-target
  (- (* 6 x) (* 9 (* x x)))

  (* (* 3 (- 2 (* x 3))) x))